Composition
Combining two functions by substituting
one function's formula in place
of each x in
the other function's formula. The composition of functions
f and g is
written f ° g,
and is read aloud "f composed with g." The formula for f ° g
is written (f ° g)(x). This is read aloud "f composed with g of x."
Note: Composition is not commutative. That is, (f ° g)(x) is usually different from (g ° f)(x). The example below illustrates this.
Example: f(x) = 3x2 + 12x – 1 and g(x) = 4x + 1
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|
1(f ° g)(x) |
= 3(4x + 1)2 + 12(4x + 1) – 1 |
|
|
= 3(16x2 + 8x + 1) + 48x + 12 – 1
= 48x2 + 72x + 14
|
|
1(g ° f)(x) |
= 4(3x2 + 12x – 1) + 1 |
|
|
= 12x2 + 48x – 4 + 1
= 12x2 + 48x – 3 |
See
also
Identity
of an operation, identity
function,
inverse, composite
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